BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

1st Edition

ISBN: 9781608408382

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 5.4, Problem 6Q

To determine

ToSolve:Thegiven below system of linear equations, and check the solutions.

3x−5y=13

x+4y=10

Expert Solution & Answer

Answer to Problem 6Q

The solution of the given system of linear equations is (x,y)=(6,1)

Explanation of Solution

Given:

The system of linear equations

3x−5y=13

x+4y=10

Concept Used:

In solving a system of linear equation by substitution method. The value of one of the unknown from any of the equation is substituted into another equation and the value of second unknown is calculated.

The calculated value of second unknown is then substituted into any of the equation to find the value of the first unknown.

Calculation:

Given the system of linear equations

3x−5y=13 - - - - - (1)

x+4y=10 - - - - - (2)

Using the Substitution method

From equation (1)

3x−5y=133x−5y+5y=13+5y Add 5y to both sides3x=13+5y3x3=133+5y3 Divide both sides by 3

x=133+5y3

Substituting the value of x from equation (1) into the equation (2) , we have

x+4y=10133+5y3+4y=10 Substitue 133+5y3 for x133+5y3+12y3=303133+5y3+12y3−133=303−133 Subtract 133 from both sides

17y3=173(17y3)(317)=(173)(317) Multiply both sides by 317y=1

Substituting y=1 into equation (1)

3x−5y=133x−5(1)=13 Substitute y=13x−5=13 3x−5+5=13+5 Add 5 to both sides

3x=183x3=183 Divide both sides by 3x=6

Therefore, the solution of the given system of linear equations is (x,y)=(6,1)

Checking

Substituting the solution (x,y)=(6,1) in left side of the first equation 3x−5y=13

3x−5y=3(6)−5(1) Substitute (x,y)=(6,1)=18−5=13 Equal to right hand side of the equation

Substituting the solution (x,y)=(6,1) in left side of the second equation x+4y=10

x+4y=6+4(1) Substitute (x,y)=(6,1)=6+4=10 Equal to right hand side of the equation

Hence, the solution is (x,y)=(6,1) verified.

Conclusion:

The solution of the given system of linear equations is (x,y)=(6,1)

Chapter 5.4, Problem 5Q

Chapter 5.4, Problem 7Q

Chapter 5 Solutions

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Prob. 6E Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Prob. 21E Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - 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ToSolve: Thegiven below system of linear equations, and check the solutions. 3 x − 5 y = 13 x + 4 y = 10

Videos

ToSolve:Thegiven below system of linear equations, and check the solutions. 3x−5y=13 x+4y=10

Answer to Problem 6Q

Explanation of Solution

Chapter 5 Solutions

ToSolve:Thegiven below system of linear equations, and check the solutions.

3x−5y=13

x+4y=10